Method and device for control of a unit for reproduction of an acoustic field

ABSTRACT

Said method for control of a reproduction unit ( 2 ) for an acoustic field with a number of reproduction elements ( 3   1  to  3   N ) is characterised in comprising: a step for establishing a finite number of coefficients representative of the temporal distribution and in the three spatial dimensions of said acoustic field, a step for determination of representative reconstruction filters for said reproduction unit ( 2 ) and at least the spatial configuration of said reproduction unit ( 2 ); a step for determination of at least one control signal (SC 1  to SC N ) for said elements ( 3   1  to  3   N ) by the application of said coefficients to said reconstruction filters and a step for providing said at least one control signal for application to said elements ( 3   1  to  3   N ) for generation of said acoustic field for reproduction.

The present invention relates to a method and a device for control of areproduction unit for an acoustic field.

Sound is a wavelike acoustic phenomenon which evolves over time and inspace. The existing techniques act mainly on the temporal aspect ofsounds, the processing of the spatial aspect being very incomplete.

Specifically, the existing high-quality reproduction systems actuallynecessitate a predetermined spatial configuration of the reproductionunit.

For example, so-called multichannel systems address different andpredetermined signals to several loudspeakers whose distribution isfixed and known.

Likewise, so-called “ambisonic” systems, which consider the directionfrom which the sounds which reach a listener originate, require areproduction unit whose configuration must comply with certainpositioning rules.

In these systems, the sound environment is regarded as an angulardistribution of sound sources about a point, corresponding to thelistening position. The signals correspond to a decomposition of thisdistribution over a basis of directivity functions called sphericalharmonics.

In the current state of development of these systems, good-qualityreproduction is possible only with a spherical distribution ofloudspeakers and a substantially regular angular distribution.

Thus, when the existing techniques are implemented with a reproductionunit whose spatial distribution is arbitrary, the quality ofreproduction is greatly impaired, in particular on account of angulardistortions.

Recent technical developments make it possible to consider a modeling intime and in the three dimensions in space of an acoustic field ratherthan the angular distribution of the sound environment.

In particular, the doctoral thesis “Représentation de champsacoustiques, application à la transmission et à la reproduction descènes sonores complexes dans un contexte multimédia” [Representation ofacoustic fields, application to the transmission and to the reproductionof complex sound scenes in a multimedia context] Université Paris VI,Jérôme Daniel, of 11 Jul. 2000, defines functions describing thewavelike characteristics of an acoustic field and allowing decompositionover a basis of functions of space and time which completely describes athree-dimensional acoustic field.

However, in this document, the theoretical solutions are inspired by theso-called “Ambisonic” systems and high-quality reproduction can beobtained only for the 5 existing regular spherical distributions. Noelement makes it possible to ensure high-quality reproduction with thehelp of an arbitrary spatial configuration of the reproduction unit.

It is therefore apparent that no system of the prior art makes itpossible to perform quality reproduction with the help of an arbitraryspatial configuration of the reproduction unit.

The aim of the invention is to remedy this problem by providing a methodand a device for determining signals for controlling a reproduction unitfor restoring an acoustic field whose spatial configuration isarbitrary.

A subject of the invention is a method of controlling a reproductionunit for restoring an acoustic field so as to obtain a reproducedacoustic field of specific characteristics substantially independent ofthe intrinsic characteristics of reproduction of said unit, saidreproduction unit comprising a plurality of reproduction elements,characterized in that it comprises at least:

a step of establishing a finite number of coefficients representative ofthe distribution in time and in the three dimensions in space of saidacoustic field to be reproduced;

a step of determining reconstruction filters representative of saidreproduction unit, comprising a substep of taking into account at leastspatial characteristics of said reproduction unit;

a step of determining at least one control signal for said elements ofsaid reproduction unit, said at least one signal being obtained by theapplication, to said coefficients, of said reconstruction filters; and

a step of delivering said at least one control signal, with a view to anapplication to said reproduction elements so as to generate saidacoustic field reproduced by said reproduction unit.

According to other characteristics:

said step of establishing a finite number of coefficients representativeof the distribution of said acoustic field to be reproduced comprises:

a step consisting in providing an input signal comprising temporal andspatial information for a sound environment; and

a step of shaping said input signal by decomposing said information overa basis of spatio-temporal functions, this shaping step making itpossible to deliver a representation of said acoustic field to bereproduced corresponding to said sound environment in the form of alinear combination of said functions;

said step of establishing a finite number of coefficients representativeof the distribution of said acoustic field to be reproduced comprises:

a step consisting in providing an input signal comprising a finitenumber of coefficients representative of said acoustic field to bereproduced in the form of a linear combination of spatio-temporalfunctions;

said spatio-temporal functions are so-called Fourier-Bessel functionsand/or linear combinations of these functions;

said substep of taking into account at least spatial characteristics ofsaid reproduction unit is carried out at least with the help ofparameters representative, for each element, of the three coordinates ofits position with respect to the center placed in the listening zone,and/or of its spatio-temporal response;

said substep of taking into account at least spatial characteristics ofsaid reproduction unit is carried out moreover with the help:

of parameters describing, in the form of weighting coefficients, aspatial window which specifies the distribution in space ofreconstruction constraints for the acoustic field; and

of a parameter describing an order of operation limiting the number ofcoefficients to be taken into account during said step of determiningreconstruction filters;

said substep of taking into account at least spatial characteristics ofsaid reproduction unit is carried out moreover with the help:

of parameters constituting a list of spatio-temporal functions whosereconstruction is imposed; and

of a parameter describing an order of operation limiting the number ofcoefficients to be taken into account during said step of determiningreconstruction filters;

said step of taking into account at least spatial characteristics ofsaid reproduction unit is carried out moreover at least with the help ofone of the parameters chosen from the group consisting:

of parameters representative of at least one of the three coordinates ofthe position of each or some of the elements, with respect to the centerplaced in the listening zone;

of parameters representative of the spatio-temporal responses of each orsome of the elements;

of a parameter describing an order of operation limiting the number ofcoefficients to be taken into account during said step of determiningreconstruction filters;

of parameters constituting a list of spatio-temporal functions whosereconstruction is imposed;

of parameters representative of the templates of said reproductionelements;

of a parameter representative of the desired local capacity ofadaptation to the spatial irregularity of the configuration of saidreproduction unit;

of a parameter defining the radiation model for said reproductionelements;

of parameters representative of the frequency response of saidreproduction elements;

of a parameter representative of a spatial window;

of parameters representative of a spatial window in the form ofweighting coefficients; and

of a parameter representative of the radius of a spatial window when thelatter is a ball;

the method comprises a calibration step making it possible to deliverall or part of the parameters used in said step of determiningreconstruction filters;

said calibration step comprises, for at least one of the reproductionelements:

a substep of acquiring signals representative of the radiation of saidat least one element in the listening region; and

a substep of determining spatial and/or acoustic parameters of said atleast one element;

said calibration step comprises:

a substep of emitting a specific signal to said at least one element ofsaid reproduction unit, said acquisition substep corresponding to theacquisition of the sound wave emitted in response by said at least oneelement; and

a substep of transforming said signals acquired into a finite number ofcoefficients representative of the sound wave emitted, so as to allowthe carrying out of said substep of determining spatial and/or acousticparameters;

said acquisition substep corresponds to a substep of receiving a numberof coefficients representative of the acoustic field generated by saidat least one element in the form of a linear combination ofspatio-temporal functions, which coefficients are used directly duringsaid substep of determining spatial and/or acoustic parameters of saidat least one element;

said calibration substep furthermore comprises a substep of determiningthe position in at least one of the three dimensions in space of said atleast one element of said reproduction unit;

said calibration step furthermore comprises a substep of determining thespatio-temporal response of said at least one element of saidreproduction unit;

said calibration step furthermore comprises a substep of determining thefrequency response of said at least one element of said reproductionunit;

the method comprises a step of simulating all or part of the parametersnecessary for carrying out said step of determining reconstructionfilters;

said simulation step comprises:

a substep of determining missing parameters from among the parametersused during said step of determining reconstruction filters;

a plurality of calculation substeps making it possible to determine thevalue or values of the missing parameter or parameters as definedpreviously as a function of the parameters received, of the frequency,and of predetermined default parameters;

said simulation step comprises a substep of determining a list ofelements of the reproduction unit that are active as a function of thefrequency, and said calculation substeps are carried out just for theelements of said list;

said simulation step comprises a substep of calculating a parameterrepresentative of the order of operation limiting the number ofcoefficients to be taken into account during said step of determiningreconstruction filters with the help of at least the position in spaceof all or part of the elements of the reproduction unit;

said simulation step comprises a step of determining parametersrepresentative of a spatial window in the form of weighting coefficientswith the help of a parameter representative of the spatial window in thespherical reference frame and/or of a parameter representative of theradius of said spatial window when the latter is a ball;

said simulation step comprises a substep of determining a list ofspatio-temporal functions whose reconstruction is imposed with the helpof the position of all or part of the elements of the reproduction unit;

the method comprises a step of input making it possible to determine allor part of the parameters used during said step of determiningreconstruction filters;

said step of determining reconstruction filters comprises:

a plurality of calculation substeps carried out for a finite number offrequencies of operation and making it possible to deliver a matrix forweighting the acoustic field, a matrix representative of the radiationof the reproduction unit, and a matrix representative of thespatio-temporal functions whose reconstruction is imposed; and

a substep of calculating a decoding matrix, carried out for a finitenumber of operating frequencies, with the help of the matrix forweighting the acoustic field, of the matrix representative of theradiation of the reproduction unit, of the matrix representative of thespatio-temporal functions whose reconstruction is imposed, and of aparameter representative of the desired local capacity of adaptation tothe spatial irregularity of the reproduction unit, representative of thereconstruction filters;

said calculation substep making it possible to deliver a matrixrepresentative of the radiation of the reproduction unit is carried outwith the help of parameters representative for each element:

of the three coordinates of its position with respect to the centerplaced in the listening zone; and/or

of its spatio-temporal response; and

said calculation substep making it possible to deliver a matrixrepresentative of the radiation of the reproduction unit is carried outmoreover with the help of parameters representative for each element ofits frequency response.

A subject of the invention is also a computer program comprising programcode instructions for the execution of the steps of the method when saidprogram is executed on a computer.

A subject of the invention is also a removable medium of the typecomprising at least one processor and a nonvolatile memory element,characterized in that said memory comprises a program comprisinginstructions for the execution of the steps of the method when saidprocessor executes said program.

The subject of the invention is also a device for controlling areproduction unit for restoring an acoustic field, comprising aplurality of reproduction elements, characterized in that it comprisesat least:

means of determining reconstruction filters representative of saidreproduction unit, adapted so as to make it possible to take intoaccount at least spatial characteristics of said reproduction unit; and

means for determining at least one control signal for said elements ofsaid reproduction unit, said at least one signal being obtained byapplication of said reconstruction filters to a finite number ofcoefficients representative of the distribution in time and in the threedimensions in space of said acoustic field to be reproduced.

According to other characteristics of the invention:

the device is associated with means for shaping an input signalcomprising temporal and spatial information for a sound environment tobe reproduced, which means are adapted for decomposing said informationover a basis of spatio-temporal functions so as to deliver a signalcomprising said finite number of coefficients representative of thedistribution in time and in the three dimensions in space of saidacoustic field to be reproduced, corresponding to said soundenvironment, in the form of a linear combination of said spatio-temporalfunctions;

said spatio-temporal functions are so-called Fourier-Bessel functionsand/or linear combinations of these functions;

said means for determining reconstruction filters receive as input atleast one of the parameters from the following parameters:

parameters representative of at least one of the three coordinates ofthe position of each or some of the elements, with respect to the centerplaced in the listening zone;

parameters representative of the spatio-temporal responses of each ofsome of the elements;

a parameter describing an order of operation limiting the number ofcoefficients to be taken into account in the means of determiningreconstruction filters;

parameters representative of the templates of said reproductionelements;

a parameter representative of the desired local capacity of adaptationto the spatial irregularity of the configuration of said reproductionunit;

a parameter defining the radiation model for said reproduction elements;

parameters representative of the frequency response of said reproductionelements;

a parameter representative of a spatial window;

parameters representative of a spatial window in the form of weightingcoefficients;

parameters representative of the radius of a spatial window when thelatter is a ball; and

parameters constituting a list of spatio-temporal functions whosereconstruction is imposed;

each of said parameters received by said means of determiningreconstruction filters is conveyed by one of the signals from the groupof the following signals:

a definition signal comprising information representative of the spatialcharacteristics of the reproduction unit;

a supplementary signal comprising information representative of theacoustic characteristics associated with the elements of thereproduction unit; and

an optimization signal comprising information relating to anoptimization strategy,

so as to deliver, with the aid of the parameters contained in thesesignals, a signal representative of said reconstruction filtersrepresentative of said reproduction unit;

the device is associated with means for determining all or part of theparameters received by said means for determining reconstructionfilters, said means comprising at least one of the following elements:

simulation means;

calibration means;

parameters input means;

said means for determining reconstruction filters are adapted fordetermining a set of filters representative of the position in space ofthe elements of the reproduction unit; and

said means of determining reconstruction filters are adapted fordetermining a set of filters representative of the room effect inducedby the listening zone.

The invention will be better understood on reading the description whichfollows, given merely by way of example and while referring to theappended drawings, in which:

FIG. 1 is a representation of a spherical reference frame;

FIG. 2 is a diagram of a reproduction system according to the invention;

FIG. 3 is a schematic diagram of the method of the invention;

FIG. 4 is a diagram detailing the calibration means;

FIG. 5 is a diagram detailing the calibration step;

FIG. 6 is a diagram of the simulation step;

FIG. 7 is a diagram of the means of determining reconstruction filters;

FIG. 8 is a diagram of the step of determining reconstruction filters;

FIG. 9 is a mode of embodiment of the step of shaping the input signal;and

FIG. 10 is a mode of embodiment of the step of determining controlsignals.

Represented in FIG. 1 in such a way as to specify the system ofcoordinates to which reference is made in the text is a conventionalspherical reference frame.

This reference frame is an orthonormal reference frame, with origin Oand comprising three axes (OX), (OY) and (OZ).

In this reference frame, a position denoted {overscore (x)} is describedby means of its spherical coordinates (r,θ,φ), where r designates thedistance with respect to the origin O and θ the orientation in thevertical plane and φ the orientation in the horizontal plane.

In such a reference frame, an acoustic field is known if at each instantt the acoustic pressure denoted p(r,θ,φ,t), whose temporal Fouriertransform is denoted P(r,θ,φ,f) where f designates the frequency, isdefined at every point.

FIG. 2 is a representation of a reproduction system according to theinvention.

This system comprises a decoder 1 controlling a reproduction unit 2which comprises a plurality of elements 3 ₁ to 3 _(N), such asloudspeakers, acoustic enclosures or any other sound source, arranged inan arbitrary manner in a listening region 4. The origin O of thereference frame, referred to as the center 5 of the reproduction unit,is placed arbitrarily in the listening region 4.

Together, the set of spatial, acoustic and electrodynamiccharacteristics is considered to be the intrinsic characteristics ofreproduction.

The system also comprises means 6 for shaping an input signal SI andmeans 7 for generating parameters comprising means 8 of simulation,means 9 of calibration and means 10 of inputting parameters.

The decoder 1 comprises means 11 for determining control signals andmeans 12 for determining reconstruction filters.

The decoder 1 receives as input a signal SI_(FB) comprising informationrepresentative of the three-dimensional acoustic field to be reproduced,a definition signal SL comprising information representative of thespatial characteristics of the reproduction unit 2, a supplementarysignal RP comprising information representative of the acousticcharacteristics associated with the elements 3 ₁ to 3 _(N) and anoptimization signal OS comprising information relating to anoptimization strategy.

The decoder emits a specific control signal sc₁ to sc_(N) destined foreach of the elements 3 ₁ to 3 _(N) of the reproduction unit 2.

Represented diagrammatically in FIG. 3 are the main steps of the methodimplemented in a system according to the invention as described withreference to FIG. 2.

The method comprises a step 20 of inputting optimization parameters, astep 30 of calibration making it possible to measure certaincharacteristics of the reproduction unit 2 and a simulation step 40.

During the parameters input step 20 implemented by the interface means10, certain parameters of the operation of the system may be definedmanually by an operator or be delivered by a suitable device.

During the calibration step 30, described in greater detail withreference to FIGS. 4 and 5, the calibration means 9 are linked in turnone by one with each of the elements 3 ₁ to 3 _(N) of the reproductionunit 2 so as to measure parameters associated with these elements.

The simulation step 40, implemented by the means 8, makes it possible tosimulate the signals of parameters necessary for the operation of thesystem which are neither input during step 20 nor measured during step30.

The means 7 for generating parameters then deliver as output thedefinition signal SL, the supplementary signal RP and the optimizationsignal OS.

Thus, steps 20, 30 and 40 make it possible to determine the set ofparameters necessary for the implementation of step 50.

Following these steps, the method comprises a step 50 of determiningreconstruction filters that is implemented by the means 12 of thedecoder 1 and makes it possible to deliver a signal FD representative ofthe reconstruction filters.

This step 50 of determining reconstruction filters makes it possible totake into account the at least spatial characteristics of thereproduction unit 2 that are defined during the steps 20 of input, 30 ofcalibration or 40 of simulation. Step 50 also makes it possible to takeinto account the acoustic characteristics associated with the elements 3₁ to 3 _(N) of the reproduction unit 2 and the information relating toan optimization strategy.

The reconstruction filters obtained on completion of step 50 aresubsequently stored in the decoder 1 so that steps 20, 30, 40 and 50 arerepeated only in case of modification of the reproduction unit 2 or ofthe optimization strategies.

During operation, the signal SI comprising temporal and spatialinformation of a sound environment to be reproduced, is provided to theshaping means 6, for example by direct acquisition or by reading arecording or by synthesis with the aid of computer software. This signalSI is shaped during a shaping step 60. On completion of this step, themeans 6 deliver to the decoder 1 a signal SI_(FB) comprising a finitenumber of coefficients representative, over a basis of spatio-temporalfunctions, of the distribution in time and in the three dimensions inspace, of an acoustic field to be reproduced corresponding to the soundenvironment to be reproduced.

As a variant, the signal SI_(FB) is provided by exterior means, forexample a microcomputer comprising synthesis means.

The invention is based on the use of a family of spatio-temporalfunctions making it possible to describe the characteristics of anyacoustic field.

In the embodiment described, these functions are so-called sphericalFourier-Bessel functions of the first kind subsequently referred to asFourier-Bessel functions.

In a zone devoid of sound sources and devoid of obstacles, theFourier-Bessel functions are solutions of the wave equation andconstitute a basis which spans all the acoustic fields produced by soundsources situated outside this zone.

Any three-dimensional acoustic field is therefore expressed as a linearcombination of Fourier-Bessel functions, according to the expression forthe inverse Fourier-Bessel transform which is expressed as:${P\left( {r,\theta,\phi,f} \right)} = {4\pi{\sum\limits_{l = 0}^{\infty}{\sum\limits_{m = {- l}}^{l}{{P_{l,m}(f)}j^{l}{j_{l}({kr})}{y_{l}^{m}\left( {\theta,\phi} \right)}}}}}$

In this equation, the terms P_(l,m)(f) are, by definition, theFourier-Bessel coefficients of the field p(r,θ,φ,t),${k = \frac{2\pi\quad f}{c}},$c is the speed of sound in air (340 ms⁻¹), j_(l)(kr) is the sphericalBessel function of the first kind of order l defined by${j_{l}(x)} = {\sqrt{\frac{\pi}{2x}}{J_{l + {1/2}}(x)}}$where J_(v)(x) is the Bessel function of the first kind of order v, andy_(l) ^(m)(θ,φ) is the real spherical harmonic of order l and of term m,with m ranging from −1 to 1, defined by:${y_{l}^{m}\left( {\theta,\phi} \right)} = \left\{ \begin{matrix}{\frac{1}{\sqrt{\pi}}{P_{l}^{m}\left( {\cos\quad\theta} \right)}{\cos\left( {m\quad\phi} \right)}} & {{{for}\quad m} > 0} \\{\frac{1}{\sqrt{2\pi}}{P_{l}^{0}\left( {\cos\quad\theta} \right)}} & {{{for}\quad m} = 0} \\{\frac{1}{\sqrt{\pi}}{P_{l}^{m}\left( {\cos\quad\theta} \right)}{\sin\left( {m\quad\phi} \right)}} & {{{for}\quad m} < 0}\end{matrix} \right.$

In this equation, the P_(l) ^(m)(x) are the associated Legendrefunctions defined by:${P_{l}^{m}(x)} = {\sqrt{\frac{{2l} + 1}{2}}\sqrt{\frac{\left( {l - m} \right)!}{\left( {l + m} \right)!}}\left( {1 - x^{2}} \right)^{m/2}\frac{\mathbb{d}^{m}}{\mathbb{d}x^{m}}{P_{l}(x)}}$with P_(l)(x) the Legendre polynomials, defined by:${P_{l}(x)} = {\frac{1}{2^{l}{l!}}\frac{\mathbb{d}^{l}}{\mathbb{d}x^{l}}\left( {x^{2} - 1} \right)^{l}}$

The Fourier-Bessel coefficients are also expressed in the temporaldomain by the coefficients p_(l,m)(t) corresponding to the inversetemporal Fourier transform of the coefficients P_(l,m)(f).

As a variant, the method of the invention uses function bases expressedas linear combinations, possibly infinite, of Fourier-Bessel functions.

During the shaping step 60, carried out by the means 6, the input signalSI is decomposed into Fourier-Bessel coefficients p_(l,m)(t) in such away as to establish the coefficients forming the signal SI_(FB).

The decomposition into Fourier-Bessel coefficients is conducted up to alimit order L defined previously to this shaping step 60 during theinput step 20.

On completion of step 60, the signal SI_(FB) delivered by the shapingmeans 6 is introduced into the means 11 for determining the controlsignals. These means 11 also receive the signal FD representative of thereconstruction filters defined by taking account in particular of thespatial configuration of the reproduction unit 2.

The coefficients of the signal SI_(FB), delivered on completion of step60, are used by the means 11 during a step 70 of determining the controlsignals sc₁ to sc_(N) for the elements of the reproduction unit 2 withthe help of the application of the reconstruction filters determinedduring step 50 to these coefficients.

The signals sc₁ to sc_(N) are then delivered so as to be applied to theelements 3 ₁ to 3 _(N) of the reproduction unit 2 which reproduce theacoustic field whose characteristics are substantially independent ofthe intrinsic characteristics of reproduction of the reproduction unit2.

By virtue of the method of the invention, the control signals sc₁ tosc_(N) are adapted to allow optimal reproduction of the acoustic fieldwhich best utilizes the spatial and/or acoustic characteristics of thereproduction unit 2, in particular the room effect, and which integratesthe chosen optimization strategy.

Thus, on account of the quasi-independence between the intrinsiccharacteristics of reproduction of the reproduction unit 2 and of theacoustic field reproduced, it is possible to render the lattersubstantially identical to the acoustic field corresponding to the soundenvironment represented by the temporal and spatial information receivedas input.

The main steps of the method of the invention will now be described ingreater detail.

During step 20 of inputting parameters an operator or a suitable memorysystem can specify all or part of the calculation parameters and inparticular:

x_(n), representative of the position of element 3 _(n) with respect tothe listening center 5; x_(n) being expressed in the spherical referenceframe by means of the coordinates r_(n), θ_(n), and φ_(n);

G_(n)(f), representative of the template of element 3 _(n) of thereproduction unit specifying the frequency band of operation of thiselement;

N_(l,m,n)(f), representative of the spatio-temporal response of theelement 3 _(n) corresponding to the acoustic field produced in thelistening region 4 by the element 3 _(n), when the latter receives animpulse signal as input;

W(r,f), describing for each frequency f considered a spatial windowrepresentative of the distribution in space of constraints ofreconstruction of the acoustic field, these constraints making itpossible to specify the distribution in space of the effort ofreconstruction of the acoustic field;

W_(l)(f), describing directly in the form of weighting of theFourier-Bessel coefficients and for each frequency f considered, aspatial window representative of the distribution in space ofconstraints of reconstruction of the acoustic field;

R(f), representative, for each frequency f considered, of the radius ofthe spatial window when the latter is a ball;

H_(n)(f), representative, for each frequency f considered, of thefrequency response of element 3 _(n);

μ(f), representative for each frequency f considered, of the desiredlocal capacity of adaptation to the spatial irregularity of theconfiguration of the reproduction unit;

{(l_(k),m_(k))}(f), constituting for each frequency f considered, a listof spatio-temporal functions whose reconstruction is imposed;

L(f), imposing, for each frequency f considered, the limit order ofoperation of the means 12 of determining reconstruction filters;

RM(f), defining, for each frequency f considered, the radiation modelfor the elements 3 ₁ to 3 _(N) of the reproduction unit 2.

The definition signal SL conveys the parameters x_(n), the supplementarysignal RP, the parameters H_(n)(f) and N_(l,m,n)(f) and the optimizationsignal OS, the parameters G_(n)(f), μ(f), {(l_(k),m_(k))}(f), L(f),W(r,f), W_(l)(f), R(f) and RM(f).

The interface means 10 implementing this step 20 are conventional typemeans such as a microcomputer or any other appropriate means.

Step 30 of calibration and the means 9 which implement it will now bedescribed in greater detail.

Represented in FIG. 4 are the details of the calibration means 9. Theycomprise a decomposition module 91, a module 92 for determining impulseresponse and a module 93 for determining calibration parameters.

The calibration means 9 are adapted to be connected to a soundacquisition device 100 such as a microphone or any other suitabledevice, and to be connected in turn one by one to each element 3 _(n) ofthe reproduction unit 2 so as to tap information off from this element.

Represented in FIG. 5 are the details of a mode of embodiment of thecalibration step 30 implemented by the calibration means 9 and making itpossible to measure characteristics of the reproduction unit 2.

During a substep 32, the calibration means 9 emit a specific signalu_(n)(t) such as a pseudo-random sequence MLS (Maximum Length Sequence)destined for an element 3 _(n). The acquisition device 100 receives,during a substep 34, the sound wave emitted by the element 3 _(n) inresponse to the receipt of the signal u_(n)(t) and transmits signalsc_(l,m)(t) representative of the wave received to the decompositionmodule 91.

During a substep 36, the decomposition module 91 decomposes the signalspicked up by the acquisition device 100 into a finite number ofFourier-Bessel coefficients q_(l,m)(t).

For example, the device 100 delivers pressure information p(t) andvelocity information {overscore (v)}(t) at the center 5 of thereproduction unit. In this case, the coefficients q_(0,0)(t) toq_(1,1)(t) representative of the acoustic field are deduced from thesignals c_(0,0)(t) to c_(1,1)(t) according to the following relations:$\begin{matrix}{{q_{0,0}(t)} = {\frac{1}{\sqrt{4\pi}}{c_{0,0}(t)}}} & {with} & {{c_{0,0}(t)} = {p(t)}} \\{{q_{1,{- 1}}(t)} = {\rho\quad c\sqrt{\frac{3}{4\pi}}{c_{1,{- 1}}(t)}}} & {with} & {{c_{1,{- 1}}(t)} = {v_{Y}(t)}} \\{{q_{1,0}(t)} = {{- \rho}\quad c\sqrt{\frac{3}{4\pi}}{c_{1,0}(t)}}} & {with} & {{c_{1,0}(t)} = {v_{Z}(t)}} \\{{q_{1,1}(t)} = {{- \rho}\quad c\sqrt{\frac{3}{4\pi}}{c_{1,1}(t)}}} & {with} & {{c_{1,1}(t)} = {v_{X}(t)}}\end{matrix}$

In these equations, v_(x)(t), v_(y)(t) and v_(z)(t) designate thecomponents of the velocity vector {overscore (v)}(t) in the orthonormalreference frame considered and ρ designates the density of the air.

When these coefficients are defined by the module 91, they are addressedto the response determination module 92.

During a substep 38, the response determination module 92 determines theimpulse responses hp_(l,m)(t) which link the Fourier-Bessel coefficientsq_(l,m)(t) and the signal emitted u_(n)(t).

The impulse response delivered by the response determination module 92is addressed to the parameters determination module 93.

During a substep 39, the module 93 deduces information on elements ofthe reproduction unit.

In the embodiment described, the parameters determination module 93determines the distance r_(n) between the element 3 _(n) and the center5 with the help of its response hp_(0,0)(t) and of the measurement ofthe time taken by the sound to propagate from the element 3 _(n) to theacquisition device 100, by virtue of delay estimation procedures withregard to the response hp_(0,0)(t).

In the embodiment described, the acquisition device 100 is able tounambiguously encode the orientation of a source in space. Thus,trigonometric relations between the 3 responses hp_(1,−1)(t),hp_(1,0)(t) and hp_(1,1)(t) involving the coordinates θ_(n), and φ_(n)are apparent for each instant t.

The module 93 determines the values hp_(1,−1), hp_(1,0) and hp_(1,1)corresponding to the values taken by the responses hp_(1,−1)(t),hp_(1,0)(t) and hp_(1,1)(t) at an arbitrarily chosen instant t such asfor example the instant for which hp_(0,0)(t) attains its maximum.

Subsequently, the module 93 estimates coordinates θ_(n) and φ_(n) withthe help of the values hp_(1,−1), hp_(1,0) and hp_(1,1) by means of thefollowing trigonometric relations: $\begin{matrix}{{\text{-}{for}\quad{hp}_{1,0}} > {0\text{:}}} & {\theta_{n} = {\arctan\left( \frac{\sqrt{{hp}_{1,{- 1}}^{2} + {hp}_{1,1}^{2}}}{{hp}_{1,0}} \right)}} \\{{\text{-}{for}\quad{hp}_{1,0}} < {0\text{:}}} & {\theta_{n} = {\pi - {\arctan\left( \frac{\sqrt{{hp}_{1,{- 1}}^{2} + {hp}_{1,1}^{2}}}{{hp}_{1,0}} \right)}}} \\{{\text{-}{for}\quad{hp}_{1,1}} > {0\text{:}}} & {\phi_{n} = {- {\arctan\left( \frac{{hp}_{1,{- 1}}}{{hp}_{1,1}} \right)}}} \\{{\text{-}{for}\quad{hp}_{1,1}} < {0\text{:}}} & {\phi_{n} = {\pi - {\arctan\left( \frac{{hp}_{1,{- 1}}}{{hp}_{1,1}} \right)}}}\end{matrix}$

These relations admit the following particular cases: $\begin{matrix}{{\text{-}{for}\quad h\quad p_{1,0}} = {{0\quad{and}\quad h\quad p_{1,1}} \neq {0\text{:}}}} & {\theta_{n} = \frac{\pi}{2}} \\{{\text{-}{for}\quad h\quad p_{1,1}} = {{0\quad{and}\quad h\quad p_{1,{- 1}}} = {{0\quad{and}\quad h\quad p_{1,0}} = {0\text{:}}}}} & {\theta_{n}\quad{and}\quad\phi_{n}\quad{are}\quad{undefined}} \\{{\text{-}{for}\quad h\quad p_{1,1}} = {{{0\quad{and}\quad h\quad p_{1,{- 1}}} \neq {0\quad{and}\quad h\quad p_{1,0}}} = {0\text{:}}}} & {\theta_{n} = \frac{\pi}{2}} \\{{\text{-}{for}\quad h\quad p_{1,1}} = {{0\quad{and}\quad h\quad p_{1,{- 1}}} \neq {0\quad{and}\quad h\quad p_{1,0}} \neq {0\text{:}}}} & {\phi_{n} = {{- {{signe}\left( {h\quad p_{1,{- 1}}} \right)}}\frac{\pi}{2}}}\end{matrix}$

Advantageously, the coordinates θ_(n), and φ_(n) are estimated overseveral instants. The final determination of the coordinates θ_(n) andφ_(n) is obtained by means of techniques of averaging between thevarious estimates.

As a variant, the coordinates θ_(n), and φ_(n) are estimated with thehelp of other responses from among the available hp_(l,m)(t) or areestimated in the frequency domain with the help of the responseshp_(l,m)(f).

Thus defined, the parameters r_(n), θ_(n), and φ_(n) are transmitted tothe decoder 1 by the definition signal SL.

In the embodiment described, the module 93 also delivers the transferfunction H_(n)(f) of each element 3 _(n), with the help of the responseshp_(l,m)(t) arising from the response determination module 92.

A solution consists in constructing the response hp′_(0,0)(t)corresponding to the selection of the part of the response hp_(0,0)(t)which comprises a non zero signal stripped of its reflections introducedby the listening region 4. The frequency response H_(n)(f) is deduced byFourier transform from the response hp′_(0,0)(t) previously windowed.The window may be chosen from the conventional smoothing windows, suchas for example rectangular, Hamming, Hanning, and Blackman.

The parameters H_(n)(f) thus defined are transmitted to the decoder 1 bythe supplementary signal RP.

In the embodiment described, the module 93 also delivers thespatio-temporal response N_(l,m,n)(f) of each element 3 _(n) of thereproduction unit 2, deduced by applying a gain adjustment and atemporal alignment of the impulse responses hp_(l,m)(t) with the help ofthe measurement of the distance r_(n) of the element 3 _(n) in thefollowing manner:η_(l,m,n)(t)=r _(n) hp _(l,m)(t+r _(n) /c)

The spatio-temporal response η_(l,m,n)(t) contains a large amount ofinformation characterizing the element 3 _(n), in particular itsposition and its frequency response. It is also representative of thedirectivity of the element 3 _(n), of its spread, and of the room effectresulting from the radiation of the element 3 _(n) in the listeningregion 4.

The module 93 applies a time windowing to the response η_(l,m,n)(t) toadjust the duration for which the room effect is taken into account. Thespatio-temporal response expressed in the frequency domain N_(l,m,n)(f)is obtained by Fourier transform of the response η_(l,m,n)(t). Thespatio-temporal response N_(l,m,n)(f) is then frequency-windowed so asto adjust the frequency band over which the room effect is taken intoaccount. The module 93 then delivers the parameters N_(l,m,n)(f) thusshaped which are provided to the decoder 1 by the supplementary signalRP.

Substeps 32 to 39 are repeated for all the elements 3 ₁ to 3 _(N) of thereproduction unit 2.

As a variant, the calibration means 9 are adapted to receive other typesof information pertaining to the element 3 _(n). For example, thisinformation is introduced in the form of a finite number ofFourier-Bessel coefficients representative of the acoustic fieldproduced by the element 3 _(n) in the listening region 4.

Such coefficients may in particular be delivered by means of acousticsimulation implementing a geometrical modeling of the listening region 4so as to determine the position of the image sources induced by thereflections due to the position of the element 3 _(n) and to thegeometry of the listening region 4.

The means of acoustic simulation receive as input the signal u_(n)(t)emitted by the module 92 and delivered, with the aid of the signalc_(l,m)(t), the Fourier-Bessel coefficients determined by superpositionof the acoustic field emitted by the element 3 _(n) and of the acousticfields emitted by the image sources when the element 3 _(n) receives thesignal u_(n)(t). In this case the decomposition module 91 performs onlya transmission of the signal c_(l,m)(t) to the module 92.

As a variant, the calibration means 9 comprise other means ofacquisition of information pertaining to the elements 3 ₁ to 3 _(N),such as laser-based position measuring means, signal processing meansimplementing beam forming techniques or any other appropriate means.

The means 9 implementing the calibration step 30 consist for example ofan electronic card or of a computer program or of any other appropriatemeans.

The details of the parameters simulation step 40 and the means 8 whichimplement it will now be described. This step is carried out for eachfrequency f of operation.

The embodiments described require the knowledge for each element 3 _(n)of its complete position described by the parameters r_(n), θ_(n), φ_(n)and/or of its spatio-temporal response described by the parametersN_(l,m,n)(f).

In a first embodiment, described with reference to FIG. 6, theparameters which are neither input, by an operator or by external means,nor measured, are simulated.

Step 40 begins with a substep 41 of determining parameters missing fromthe signals RP, SL and OS received.

During a substep 42, the parameter H_(n)(f) representative of theresponse of the elements of the reproduction unit 2 takes the defaultvalue 1.

During a substep 43, the parameter G_(n)(f) representative of thetemplates of the elements of the reproduction unit 2 is determined bythresholding on the parameter H_(n)(f) in the case where the latter ismeasured, defined by the user, or provided by external means, otherwise,G_(n)(f) takes the default value 1.

Step 40 then comprises a substep 44 of determining the active elementsat the frequency f considered.

During this substep, a list {n*}(f) of elements of the reproduction unitthat are active at the frequency f is determined, these elements beingthose whose template G_(n)(f) is non zero for this frequency. The list{n*}(f) comprises N_(f) elements and it is transmitted to the decoder 1by the optimization signal OS. It is used to select the parameterscorresponding to the active elements at each frequency f among the setof parameters. The parameters of index n* correspond to the n^(th)active element at the frequency f.

During a substep 45, the parameter L(f) representative of the order ofoperation of the module for determining the filters at the currentfrequency f, is determined in the following manner:

the simulation means 8 calculate the smallest angle a_(min) formed by apair of elements of the reproduction unit by means of a trigonometricrelation, such as for example:a _(n1*,n2*) =a cos (sin θ_(n1*) sin θ_(n2*) cos (φ_(n1*)−φ_(n2*))+cosθ_(n1*) cos θ_(n2*))a _(min)=min(a _(n1*,n2*))among the set of pairs (n1*, n2*) such that n1*≠n2*;

the simulation means 9 determine the maximum order L(f) which is thelargest integer obeying the relationL(f)<π/a _(min).

During a substep 46, the parameter RM(f) defining the radiation modelfor the elements constituting the reproduction unit, is determinedautomatically taking the spherical radiation model as default.

During a substep 47, the parameter W_(l)(f) which describes the spatialwindow representative of the distribution in space of constraints ofreconstruction of the acoustic field in the form of weighting ofFourier-Bessel coefficients is determined in the following manner:

if the parameter W(r,f) representative of the spatial window in thespherical reference frame is provided or input, W_(l)(f) is deduced fromits value by applying the expression:W_(l)(f) = 16π²∫₀^(∞)W(r, f)j_(l)²(kr)r²  𝕕r

and if the parameter R(f), which represents a radius when the spatialwindow is a ball of radius R(f), is provided by external means or input,W_(l)(f) is deduced from its value by applying the expression:${W_{l}(f)} = {8\pi^{2}{R^{3}(f)}\left( {{j_{l}^{2}\left( {{kR}(f)} \right)} + {j_{l + 1}^{2}\left( {{kR}(f)} \right)} - {\frac{{2l} + 1}{{kR}(f)}{j_{l}\left( {{kR}(f)} \right)}{j_{l + 1}\left( {{kR}(f)} \right)}}} \right)}$otherwise, W_(l)(f) is deduced from L(f), by applying the expression:${W_{l}(f)} = {8\pi^{2}{R^{3}\left( {{j_{l}^{2}({kR})} + {j_{l + 1}^{2}({kR})} - {\frac{{2l} + 1}{kR}{j_{l}({kR})}{j_{l + 1}({kR})}}} \right)}\quad{with}}$$R = \frac{{L(f)}c}{2\pi\quad f}$

As a variant, if the spatial window is not specified, the simulationmeans 8 allocate the parameter W_(l)(f) a default value, for example aHamming window of size 2L(f)+1, evaluated in l.

The parameter W_(l)(f) is determined for the values of l ranging from 0to L(f).

During a substep 48, the parameter {(l_(k), m_(k))}(f) is deduced fromthe parameters L(f) and {overscore (x)}_(n*), in the following manner:

Firstly, the means 9 calculate the coefficientsG _(l,m,n*) =y _(l) ^(m)(θ_(n*),φ_(n*))where (θ_(n*),φ_(n*)) is the direction of the reproduction element 3_(n*).

Secondly, the means 9 calculate the coefficients$G_{l,m} = \sqrt{\sum\limits_{n = l}^{N_{f}}G_{l,m,n^{*}}^{2}}$

Thirdly, the means 8 calculate, with the aid of a supplementaryparameter ε, the list of parameters {(l_(k), m_(k))}(f), referred to asC and which is initially empty. For each value of the order l, startingat 0, the means 8 carry out the following substeps:

search for G_(l)=max(G_(l,m));

determination of the list C_(l) of coefficients (l,m) such that G_(l,m)(in dB) lies between G_(l)−ε (in dB) and G_(l) (in dB).

If the sum of the number of terms in C and of the number of terms inC_(l) is greater than or equal to the number N_(f) of activereproduction elements at the frequency f, the list C is complete,otherwise, C_(l) is added to C and the search for G_(l) is restarted forl+1.

In the case where the elements 3 _(l*) to 3 _(Nf*) are in a horizontalplane and where the list of the {(lk, m_(k))}(f) is neither input, norprovided, the simulation means 8 perform a simplified processing:

The list of coefficients {(l_(k), m_(k))}(f) takes the form:

-   -   {(0,0),(1,−1),(1,1),(2,−2),(2,2) . . .        (L_(l),−L_(l)),(L₁,L_(l))}        where L_(l) is chosen so that the number of elements in this        list is less than the number N_(f) of elements 3 _(n*) active at        the frequency f. The value taken by L_(l) may be the integer        part of (N_(f)−1)/2, but it is preferable to take a smaller        value for L_(l).

During a substep 49, the parameter μ(f), which represents at the currentfrequency f the desired local capacity of adaptation, varying between 0and 1, is determined automatically, taking the default value 0.7 forexample.

Thus, the simulation means 9 make it possible, during step 40, tosupplement the signals SL, RP and OS in such a way as to deliver to themeans 12 for determining reconstruction filters the set of parametersnecessary for their implementation.

As a function of the parameters input or measured, some of thesimulation substeps described are not carried out.

The simulation step 40 consisting of the set of substeps 41 to 49, isrepeated for all the frequencies considered. As a variant, each substepis carried out for all the frequencies before going to the next substep.

In another embodiment, all the parameters involved are provided to thedecoder 1 and step 40 then comprises only the substep 41 of receivingand verifying the signals SL, RP and OS and the substep 44 ofdetermining the active elements at the frequency f considered.

The simulation means 8 implementing step 40 are for example computerprograms or electronic cards dedicated to such an application or anyother appropriate means.

Step 50 of determining reconstruction filters and the means 12 whichimplement it will now be described in greater detail.

Represented in FIG. 7 are the means 12 of determining reconstructionfilters which comprise a module 82 for determining transfer matriceswith the help of the parameters of the signals SL, RP and OS as well asthe means 84 for determining a decoding matrix D*.

The means 12 also comprise a module 86 for storing the response of thereconstruction filters and a module 88 for parameterizing reconstructionfilters.

Represented in FIG. 8 are the details of step 50 for determiningreconstruction filters.

Step 50 is repeated for each frequency of operation and comprises aplurality of substeps for determining matrices representative of theparameters defined previously.

Step 50 of determining reconstruction filters comprises a substep 51 ofdetermining a matrix W for weighting the acoustic field with the help ofthe signals L(f) and W_(l)(f).

W is a diagonal matrix of size (L(f)+1)² containing the weightingcoefficients W_(l)(f) and in which each coefficient W_(l)(f) is found2l+1 times in succession on the diagonal. The matrix W therefore has thefollowing form: $W = \begin{bmatrix}{W_{0}(f)} & 0 & \ldots & \ldots & \ldots & \ldots & \ldots & 0 \\0 & {W_{1}(f)} & ⋰ & \quad & \quad & \quad & \quad & \vdots \\\vdots & ⋰ & {W_{1}(f)} & ⋰ & \quad & \quad & \quad & \vdots \\\vdots & \quad & ⋰ & {W_{1}(f)} & ⋰ & \quad & \quad & \vdots \\\vdots & \quad & \quad & ⋰ & ⋰ & ⋰ & \quad & \vdots \\\vdots & \quad & \quad & \quad & ⋰ & {W_{L}(f)} & ⋰ & \vdots \\\vdots & \quad & \quad & \quad & \quad & ⋰ & ⋰ & 0 \\0 & \ldots & \ldots & \ldots & \ldots & \ldots & 0 & {W_{L}(f)}\end{bmatrix}$

Likewise, step 50 comprises a substep 52 of determining a matrix Mrepresentative of the radiation of the reproduction unit with the helpof the parameters N_(l,m,n*)(f), RM(f), H_(n*)(f), {overscore (x)}_(n*),and L(f).

M is a matrix of size (L(f)+1)² by N_(f), consisting of elementsM_(l,m,n*), the indices l,m designating row l²+l+m and n* designatingcolumn n. The matrix M therefore has the following form:$\quad\begin{bmatrix}M_{0,0,1^{*}} & M_{0,0,2^{*}} & \ldots & M_{0,0,N_{f}^{*}} \\M_{1,{- 1},1^{*}} & M_{1,{- 1},2^{*}} & \ldots & M_{1,{- 1},N_{f}^{*}} \\M_{1,0,1^{*}} & M_{1,0,2^{*}} & \ldots & M_{1,0,N_{f}^{*}} \\M_{1,1,1^{*}} & M_{1,1,2^{*}} & \ldots & M_{1,1,N_{f}^{*}} \\\vdots & \vdots & \quad & \vdots \\M_{L,{- L},1^{*}} & M_{L,{- L},2^{*}} & \ldots & M_{L,{- L},N_{f}^{*}} \\\vdots & \vdots & \quad & \vdots \\M_{L,0,1^{*}} & M_{L,0,2^{*}} & \ldots & M_{L,0,N_{f}^{*}} \\\vdots & \vdots & \quad & \vdots \\M_{L,L,1^{*}} & M_{L,L,2^{*}} & \ldots & M_{L,L,N_{f}^{*}}\end{bmatrix}$

The elements M_(l,m,n*) are obtained as a function of the radiationmodel RM(f):

-   -   if RM(f) defines a plane wave radiation model        M _(l,m,n*) =y _(l) ^(m)(θ_(n*),φ_(n*))H _(n*)(f)    -   if RM(f) defines a spherical wave radiation model        M _(l,m,n*) =y _(l) ^(m)(θ_(n*),φ_(n*))H _(n*)(f)ξ_(l)(r _(n*)        ,f)    -   if RM(f) defines a model using the measurements performed of the        spatio-temporal responses, with recourse to the plane wave model        for the missing measurements, then M_(l,m,n*)=N_(l,m,n*)(f) for        the indices l,m,n* provided and the current frequency f. The        remainder of the M_(l,m,n*) is determined according to the        relation:        M _(l,m,n*) =y _(l) ^(m)(θ_(n*),φ_(n*))H _(n*)(f)    -   if RM(f) defines a model using the measurements performed of the        spatio-temporal responses, with recourse to the spherical wave        model for the missing measurements, then        M_(l,m,n*)=N_(l,m,n*)(f) for the indices l,m,n* provided and the        current frequency f. The remainder of the M_(l,m,n*) is        determined according to the relation:

M _(l,m,n*) =y _(l) ^(m)(θ_(n*),φ_(n*))H _(n*)(f)ξ_(l)(r _(n*) ,f)

In these expressions ξ_(l)(r_(n*),f) is defined by the expression:${\xi_{l}\left( {r_{n^{*}},f} \right)} = {\sum\limits_{k = 0}^{l}{\frac{\left( {l + k} \right)!}{2^{k}{k!}{\left( {l - k} \right)!}}\left( \frac{{j2\pi}\quad r_{n^{*}}f}{c} \right)^{- k}}}$

The matrix M thus defined is representative of the radiation of thereproduction unit. In particular, M is representative of the spatialconfiguration of the reproduction unit.

When the method uses the coefficients N_(l,m,n)(f), the matrix M isrepresentative of the spatio-temporal responses of the elements 3 ₁ to 3_(N) and therefore in particular of the room effect induced by thelistening region 4.

Step 50 also comprises a substep 53 of determining a matrix Frepresentative of the Fourier-Bessel functions, perfect reconstructionof which is demanded. This matrix is determined with the help of theparameter L(f), as well as the parameters {(l_(k),m_(k))}(f) in thefollowing manner.

With the help of the list {(l_(k),m_(k))}(f), calling K the number ofelements (l_(k),m_(k)) of the list {(l_(k),m_(k))}(f), the matrix Fconstructed is of size K by (L(f)+1)². Each row k of the matrix Fcontains a 1 in column l_(k) ²+l_(k)+m_(k), and 0s elsewhere. Forexample, for a configuration of the reproduction unit of so-called “5.1”type, whose list {(l_(k),m_(k))}(f) can take the form {(0,0), (1,−1),(1,1)}, the matrix F may be written: $F = \begin{bmatrix}1 & 0 & 0 & 0 & 0 & 0 & 0 & \ldots & 0 \\0 & 1 & 0 & 0 & 0 & 0 & 0 & \ldots & 0 \\0 & 0 & 0 & 1 & 0 & 0 & 0 & \ldots & 0\end{bmatrix}$

When the parameter μ(f) is zero, the decoder 1 reproduces only theFourier-Bessel functions enumerated by the parameters{(l_(k),m_(k))}(f), the others being ignored. When μ(f) is set to 1, thedecoder reproduces perfectly the Fourier-Bessel functions designated by{(l_(k),m_(k))}(f) but reproduces moreover partially numerous otherFourier-Bessel functions among those available up to order L(f) so thatglobally the reconstructed field is closer to that described as input.This partial reconstruction allows the decoder 1 to accommodatereproduction configurations that are very irregular in their angulardistribution.

Substeps 51 to 53 implemented by the module 82 can be executedsequentially or simultaneously.

Step 50 of determining reconstruction filters thereafter comprises asubstep 54 of taking into account the set of parameters determinedpreviously, implemented by the module 84 so as to deliver a decodingmatrix D* representative of the reconstruction filters.

This matrix D* is delivered with the help of the matrices M, F, W and ofthe parameter μ(f) according to the following expression:D*=μAM ^(T) W+AM ^(T) F ^(T)(FMAM ^(T) F ^(T))⁻¹ F(I _((L+1)) ₂ −μMAM^(T) W)with A=((1−μ)I _(N) +μM ^(T) WM) ⁻¹where M^(T) designates the matrix which is the conjugate transpose of M.

The elements D*_(n,l,m) of the matrix D* are organized in the followingmanner: $\quad\begin{bmatrix}D_{1,0,0}^{*} & D_{1,1,{- 1}}^{*} & D_{1,1,0}^{*} & D_{1,1,1}^{*} & \ldots & D_{1,L,{- L}}^{*} & \ldots & D_{1,L,0}^{*} & \ldots & D_{1,L,L}^{*} \\D_{2,0,0}^{*} & D_{2,1,{- 1}}^{*} & D_{2,1,0}^{*} & D_{2,1,1}^{*} & \ldots & D_{2,L,{- L}}^{*} & \ldots & D_{2,L,0}^{*} & \ldots & D_{2,L,L}^{*} \\\vdots & \vdots & \vdots & \vdots & \quad & \vdots & \quad & \vdots & \quad & \vdots \\D_{N_{f},0,0}^{*} & D_{N_{f},1,{- 1}}^{*} & D_{N_{f},1,0}^{*} & D_{N_{f},1,1}^{*} & \ldots & D_{N_{f},L,{- L}}^{*} & \ldots & D_{N_{f},L,0}^{*} & \ldots & D_{N_{f},L,L}^{*}\end{bmatrix}$

The matrix D* is therefore representative of the configuration of thereproduction unit, of the acoustic characteristics associated with theelements 3 ₁ to 3 _(N) and of the optimization strategies.

In the case where the method uses the coefficients N_(l,m,n)(f), thematrix D* is representative in particular of the room effect induced bythe listening region 4.

Subsequently, during a substep 55, the module 86 for storing theresponse of the reconstruction filters at the current frequency fsupplements for the frequency f the matrix D(f) representative of thefrequency response of the reconstruction filters, by receiving thematrix D* as input. The elements of the matrix D* are stored in thematrix D(f), by inverting the method, described previously withreference to FIG. 6, for determining the list {n*}(f). More precisely,each element D*_(n,l,m) of the matrix D* is stored in the elementD_(n*,l,m)(f) of the matrix D(f). The elements of D(f) that are notdetermined on completion of this substep are fixed at zero.

Such a use of the list {n*}(f) makes it possible to take account ofheterogeneous templates of the reproduction elements 3 ₁ to 3 _(N).

The elements D_(n,l,m)(f) of the matrix D(f) are organized in thefollowing manner: $\quad\begin{bmatrix}{D_{1,0,0}(f)} & {D_{1,1,{- 1}}(f)} & {D_{1,1,0}(f)} & {D_{1,1,1}(f)} & \ldots & {D_{1,L,{- L}}(f)} & \ldots & {D_{1,L,0}(f)} & \ldots & {D_{1,L,L}(f)} \\{D_{2,0,0}(f)} & {D_{2,1,{- 1}}(f)} & {D_{2,1,0}(f)} & {D_{2,1,1}(f)} & \ldots & {D_{2,L,{- L}}(f)} & \ldots & {D_{2,L,0}(f)} & \ldots & {D_{2,L,L}(f)} \\\vdots & \vdots & \vdots & \vdots & \quad & \vdots & \quad & \vdots & \quad & \vdots \\{D_{N,0,0}(f)} & {D_{N,1,{- 1}}(f)} & {D_{N,1,0}(f)} & {D_{N,1,1}(f)} & \ldots & {D_{N,L,{- L}}(f)} & \ldots & {D_{N,L,0}(f)} & \ldots & {D_{N,L,L}(f)}\end{bmatrix}$

The set of substeps 51 to 55 is repeated for all the frequencies fconsidered and the results are stored in the storage module 86. Oncompletion of this processing, the matrix D(f) representative of thefrequency responses of the set of reconstruction filters is addressed tothe module 88 for parameterizing reconstruction filters.

During a substep 58, the reconstruction filters parameterization module88 then provides the signal FD representative of the reconstructionfilters, by receiving the matrix D(f) as input. Each elementD_(n,l,m)(f) of the matrix D(f) is a reconstruction filter which isdescribed in the signal FD by means of parameters which may take variousforms.

For example, the parameters of the signal FD that are associated witheach filter D_(n,l,m)(f) may take the following forms:

a frequency response, whose parameters are directly the values ofD_(n,l,m)(f) for certain frequencies f:

a finite impulse response, whose parameters d_(n,l,m)(t) are calculatedby inverse temporal Fourier transform of D_(n,l,m)(f). Each impulseresponse d_(n,l,m)(t) is sampled and then truncated to a lengthparticular to each response; or

coefficients of an infinite impulse response recursive filter calculatedwith the help of the D_(n,l,m)(f) with conventional adaptationprocedures.

Thus, on completion of step 50 the means 12 for determiningreconstruction filters deliver a signal FD to the means 11 fordetermining control signals.

In this embodiment, this signal FD is representative of the followingparameters:

spatial configuration of the elements of the reproduction unit;

acoustic characteristics associated with the elements of thereproduction unit, in particular the frequency responses and thespatio-temporal responses representative, among other things, of theroom effect induced by the listening region 4;

optimization strategies, in particular the spatio-temporal functionsupon which one imposes the reconstruction, the distribution in space ofconstraints of reconstruction of the acoustic field and the desiredlocal capacity of adaptation to the spatial irregularity of theconfiguration of the reproduction unit 2.

The means 12 for determining reconstruction filters may be embodied inthe form of software dedicated to this function or else be integratedinto an electronic card or any other appropriate means.

Step 60 of shaping the input signal will now be described in greaterdetail.

When the system is implemented, it receives the input signal SI whichcomprises temporal and spatial information of a sound environment to bereproduced. This information may be of several sorts, in particular:

a sound environment coded according to an angular distribution such asfor example the format commonly dubbed “B format”;

a description of a sound environment by means of position informationfor virtual sources which make up the sound environment and signalsemitted by these sources;

a sound environment coded in multichannel mode, that is to say by meansof signals intended to power loudspeakers whose angular distribution isfixed and known and which includes in particular the so-called “7.1”,“5.1” quadriphonic, stereophonic and monophonic techniques;

a sound environment given by its acoustic field in the form ofFourier-Bessel coefficients.

As was stated with reference to FIG. 3, during step 60, the shapingmeans 6 receive the input signal SI and decompose it into Fourier-Besselcoefficients representative of an acoustic field corresponding to thesound environment described by the signal SI. These Fourier-Besselcoefficients are delivered to the decoder 1 by the signal SI_(FB).

As a function of the sort of input signal SI, the shaping step 60varies.

With reference to FIG. 9, the decomposition into Fourier-Besselcoefficients will now be described in the case where the soundenvironment is coded in the signal SI in the form of the description ofa sound scene by means of position information for the virtual sourcesof which it is composed and of the signals emitted by these sources.

A matrix E makes it possible to allocate a radiation model, for examplea spherical wave model, to each virtual source s. E is a matrix of size(L+1)² by S, where S is the number of sources present in the scene and Lis the order to which the decomposition is conducted. The position of asource s is designated by its spherical coordinates r_(s), θ_(s) andφ_(s). The elements E_(l,m,s) of the matrix E may be written in thefollowing manner:${E_{l,m,s}(f)} = {\frac{1}{r_{s}}{\mathbb{e}}^{{- 2}{\pi j}\quad r_{s}{f/c}}{y_{l}^{m}\left( {\theta_{s},\phi_{s}} \right)}{\xi_{l}\left( {r_{s},f} \right)}}$

Also introduced is the vector Y which contains the temporal Fouriertransforms Y_(s)(f) of the signals y_(s)(t) emitted by the sources. Ymay be written:Y=[Y₁(f)Y₂(f) . . . Y_(s)(f)]^(t)

The Fourier-Bessel coefficients P_(l,m)(f) are placed in a vector P ofsize (L+1)², where the 2l+1 terms of order l are placed one afteranother in ascending order l. The coefficient P_(l,m)(f) is thus theelement of index l²+l+m of the vector P which may be written:P=EY

As represented with reference to FIG. 9, the obtaining of theFourier-Bessel coefficients P_(l,m)(f), constituting the signal SI_(FB),corresponds to a filtering of each signal Y_(s)(f) by means of thefilter E_(l,m,s)(f), then by summing the results. The coefficientsP_(l,m)(f) are therefore expressed in the following manner:${P_{l,m}(f)} = {\sum\limits_{s = 1}^{S}{{Y_{s}(f)}{E_{l,m,s}(f)}}}$

Deployment of the filters E_(l,m,s)(f) may be effected according toconventional filtering procedures, such as for example:

filtering in the frequency domain;

filtering with the aid of a finite impulse response filter; or

filtering with the aid of an infinite impulse response filter. It is amatter of the most direct procedure which consists in deducing arecursive filter from the expression E_(l,m,s)(f), for example with theaid of a bilinear transform.

In the case where the signal SI corresponds to the representation of asound environment according to a multichannel format, the shaping means6 perform the operations described hereinafter.

A matrix S makes it possible to allocate to each channel c a radiationsource, for example a plane wave source whose direction of origination(θ_(c),φ_(c)) corresponds to the direction of the reproduction elementassociated with the channel c in the multichannel format considered. Sis a matrix of size (L+1)² by C, where C is the number of channels. Theelements S_(l,m,c) of the matrix S may be written:S _(l,m,c) =y _(l) ^(m)(θ_(c),φ_(c))

Also defined is the vector Y which contains the signals y_(c)(t)corresponding to each channel. Y may be written:Y=[y₁(t) y₂(t) . . . y_(c)(t)]^(t)

The Fourier-Bessel coefficients p_(l,m)(t) grouped together aspreviously in the vector P are obtained through the relation:P=SY

Each Fourier-Bessel coefficient p_(l,m)(t) constituting the signalSI_(FB) is obtained by linear combination of the signals y_(c)(t):${p_{l,m}(t)} = {\sum\limits_{c = 1}^{C}{{y_{c}(t)}S_{l,m,c}}}$

In the case where the signal SI corresponds to the angular descriptionof a sound environment according to the B format, the four signals W(t),X(t), Y(t) and Z(t) of this format decompose by applying simple gains:${p_{0,0}(t)} = {\frac{1}{\sqrt{4\pi}}{W(t)}}$${p_{1,1}(t)} = {\sqrt{\frac{3}{8\pi}}{X(t)}}$${p_{1,{- 1}}(t)} = {{- \sqrt{\frac{3}{8\pi}}}{Y(t)}}$${p_{1,0}(t)} = {\sqrt{\frac{3}{8\pi}}{Z(t)}}$

Finally, in the case where the signal SI corresponds to a description ofthe acoustic field in the form of the Fourier-Bessel coefficients, step60 consists simply of signal transmission.

Thus, on completion of the shaping step 60, the means 6 deliver,destined for the means 11 for determining control signals, a signalSI_(FB) corresponding to the decomposition of the acoustic field to bereproduced into a finite number of Fourier-Bessel coefficients.

The means 6 may be embodied in the form of dedicated computer softwareor else be embodied in the form of a dedicated computing card or anyother appropriate means.

The step 70 of determining control signals will now be described ingreater detail.

The means 11 for determining control signals receive as input the signalSI_(FB) corresponding to the Fourier-Bessel coefficients representativeof the acoustic field to be reproduced and the signal FD representativeof the reconstruction filters arising from the means 12. As statedpreviously, the signal FD integrates parameters characteristic of thereproduction unit 2.

With the help of this information, during step 70, the means 11determine the signals sc₁(t) to sc_(N)(t) delivered destined for theelements 3 ₁ to 3 _(N). These signals are obtained by the application tothe signal SI_(FB) of the reconstruction filters, of frequency responseD_(n,l,m)(f), and transmitted in the signal FD.

The reconstruction filters are applied in the following manner:${V_{n}(f)} = {\sum\limits_{l = 0}^{L}{\sum\limits_{m = {- l}}^{l}{{P_{l,m}(f)}{D_{n,l,m}(f)}}}}$with P_(l,m)(f) the Fourier-Bessel coefficients constituting the signalSI_(FB) and V_(n)(f) defined by:${V_{n}(f)} = {\frac{{SC}_{n}(f)}{r_{n}}{\mathbb{e}}^{{- 2}{\pi j}\quad r_{n}{f/c}}}$where SC_(n)(f) is the temporal Fourier transform of sc_(n)(t).

According to the form of the parameters of the signal FD, each filteringof the P_(l,m)(f) by D_(n,l,m)(f) can be carried out according toconventional filtering procedures, such as for example:

the signal FD provides the frequency responses D_(n,l,m)(f) directly,and the filtering is performed in the frequency domain, for example,with the aid of the usual block convolution techniques;

the signal FD provides the finite impulse responses d_(n,l,m)(t), andthe filtering is performed in the time domain by convolution; or

the signal FD provides the coefficients of infinite impulse responserecursive filters, and the filtering is performed in the time domain bymeans of recurrence relations.

Represented in FIG. 10 is the case of the finite impulse responsefilter.

The number of samples individual to each response d_(n,l,m)(t) isdefined T_(n,l,m), this leading to the following convolution expression:${v_{n}\lbrack t\rbrack} = {\sum\limits_{l = 0}^{L}{\sum\limits_{m = {- l}}^{l}{\sum\limits_{\tau = 0}^{T_{n,l,m} - 1}{{d_{n,l,m}\lbrack\tau\rbrack}{p_{l,m}\left\lbrack {t - \tau} \right\rbrack}}}}}$

Step 70 terminates with an adjustment of the gains and the applicationof delays so as to temporally align the wavefronts of the elements 3 ₁to 3 _(N) of the reproduction unit 2 with respect to the elementfurthest away. The signals sc₁(t) to sc_(N)(t) intended to feed theelements 3 ₁ to 3 _(N) are deduced from the signals v₁(t) to v_(N)(t)according to the expression:${{sc}_{n}(t)} = {r_{n}\quad{v_{n}\left( {t - \frac{{\max\left( r_{n} \right)} - r_{n}}{c}} \right)}}$

Each element 3 ₁ to 3 _(N) therefore receives a specific control signalsc₁ to sc_(N) and emits an acoustic field which contributes to theoptimal reconstruction of the acoustic field to be reproduced. Thesimultaneous control of the whole set of elements 3 ₁ to 3 _(N) allowsoptimal reconstruction of the acoustic field to be reproduced.

Furthermore, the system described can also operate in simplified modes.

For example, in a first simplified embodiment, during step 50, themodule 12 for determining filters receives only the followingparameters:

{overscore (x)}_(n) representative of the position of the element 3 _(n)of the reproduction unit 2;

W_(l) describing, directly in the form of weighting of theFourier-Bessel coefficients, a spatial window representative of thedistribution in space of constraints of reconstruction of the acousticfield; and

L, imposing the limit order of operation of the means 12 for determiningreconstruction filters.

In this simplified mode, these parameters are independent of thefrequency and the elements 3 ₁ to 3 _(N) of the reproduction unit areactive and assumed to be ideal for all the frequencies. The substeps ofstep 50 are therefore carried out once only. During substep 52, thematrix M is constructed with the help of a plane wave radiation model.The elements M_(l,m,n) of the matrix M simplify into:M _(l,m,n) =y _(l) ^(m)(θ_(n),φ_(n))

In this simplified mode, μ=1 and the list {(l_(k),m_(k))}(f) contains noterms. During substep 54, the module 84 then determines the matrix Ddirectly according to the simplified expression:D=(M ^(T) WM)⁻¹ M ^(T) W

The storage of the response of the reconstruction filters is no longernecessary, and substep 55 is not carried out. Likewise, the filtersdescribed in the matrix D having simple gains, substep 58 is no longercarried out and the module 84 provides the signal FD directly.

During step 70, the determination of the drive signals is performed inthe time domain and corresponds to simple linear combinations of thecoefficients p_(l,m)(t), followed by a temporal alignment according tothe expression:${{sc}_{n}(t)} = {r_{n}\quad{v_{n}\left( {t - \frac{{\max\left( r_{n} \right)} - r_{n}}{c}} \right)}\quad{with}}$${v_{n}(t)} = {\sum\limits_{l = 0}^{L}{\sum\limits_{m = {- l}}^{l}{{p_{l,m}(t)}D_{n,l,m}}}}$

The module 11 then provides the drive signals sc₁(t) to sc_(N)(t)intended for the reproduction unit.

In another simplified embodiment, during step 50, the module 12 fordetermining filters receives the following parameters as input:

x_(n), representative of the position of the element 3 _(n) of thereproduction unit 2;

{(l_(k),m_(k))}, constituting the list of spatio-temporal functionswhose reconstruction is imposed; and

L, imposing the order of operation of the means 12 for determiningreconstruction filters.

In this simplified mode, the parameters are independent of the frequencyand the elements 3 ₁ to 3 _(N) of the reproduction unit are active andassumed to be ideal for all the frequencies. The substeps of step 50 aretherefore carried out once only. During substep 52, the matrix M isconstructed with the help of a plane wave radiation model. The elementsM_(l,m,n) of the matrix M simplify into:M _(l,m,n) =y _(l) ^(m)(θ_(n),φ_(n))

Substep 53 of determining the matrix F remains unchanged. In thissimplified mode μ=0 and during substep 54, the module 84 determines thematrix D directly according to the simplified expression:D=M ^(T) F ^(T)(FMM ^(T) F ^(T))⁻¹ F

The storage of the response of the reconstruction filters is no longernecessary, and substep 55 is not carried out. Likewise, the filtersdescribed in the matrix D having simple gains, substep 58 is no longercarried out and the module 84 provides the signal FD directly.

During step 70, the determination of the drive signals is performed inthe time domain and corresponds to simple linear combinations of thecoefficients p_(l,m)(t), followed by a temporal alignment according tothe expression:${{sc}_{n}(t)} = {r_{n}\quad{v_{n}\left( {t - \frac{{\max\left( r_{n} \right)} - r_{n}}{c}} \right)}\quad{with}}$${v_{n}(t)} = {\sum\limits_{l = 0}^{L}{\sum\limits_{m = {- l}}^{l}{{p_{l,m}(t)}D_{n,l,m}}}}$

The module 11 then provides the drive signals sc₁(t) to sc_(N)(t)intended for the reproduction unit.

It is apparent that according to the invention, the control signals sc₁to sc_(N) are adapted to best utilize the spatial characteristics of thereproduction unit 2, the acoustic characteristics associated with theelements 3 ₁ to 3 _(N) and the optimization strategies in such a way asto reconstruct a high-quality acoustic field.

It is therefore apparent that the method implemented makes it possiblein particular to obtain optimum reproduction of a three-dimensionalacoustic field regardless of the spatial configuration of thereproduction unit 2.

The invention is not limited to the embodiments described.

In particular, the method of the invention can be implemented by digitalcomputers such as one or more computer processors or digital signalprocessors (DSP).

It may also be implemented with the help of a general platform such as apersonal computer.

It is also possible to devise an electronic card intended to be insertedinto another element and adapted for storing and executing the method ofthe invention. For example, such an electronic card is integrated into acomputer.

In other embodiments, all or part of the parameters necessary for theexecution of the step of determining reconstruction filters is extractedfrom prerecorded memories or is delivered by another apparatus dedicatedto this function.

1. A method of controlling a reproduction unit for restoring an acousticfield so as to obtain a reproduced acoustic field of specificcharacteristics substantially independent of the intrinsiccharacteristics of reproduction of said unit, said reproduction unitcomprising a plurality of reproduction elements, wherein it comprises atleast: a step of establishing a finite number of coefficientsrepresentative of the distribution in time and in the three dimensionsin space of said acoustic field to be reproduced; a step of determiningreconstruction filters representative of said reproduction unit,comprising a substep of taking into account at least spatialcharacteristics of said reproduction unit; a step of determining atleast one control signal for said elements of said reproduction unit,said at least one signal being obtained by the application, to saidcoefficients, of said reconstruction filters; and a step of deliveringsaid at least one control signal, with a view to an application to saidreproduction elements so as to generate said acoustic field reproducedby said reproduction unit.
 2. The method as claimed in claim 1, whereinsaid step of establishing a finite number of coefficients representativeof the distribution of said acoustic field to be reproduced comprises: astep consisting in providing an input signal comprising temporal andspatial information for a sound environment; and a step of shaping saidinput signal by decomposing said information over a basis ofspatio-temporal functions, this shaping step making it possible todeliver a representation of said acoustic field to be reproducedcorresponding to said sound environment in the form of a linearcombination of said functions.
 3. The method as claimed in claim 1,wherein said step of establishing a finite number of coefficientsrepresentative of the distribution of said acoustic field to bereproduced comprises: a step consisting in providing an input signalcomprising a finite number of coefficients representative of saidacoustic field to be reproduced in the form of a linear combination ofspatio-temporal functions.
 4. The method as claimed in claim 2, whereinsaid spatio-temporal functions are so-called Fourier-Bessel functionsand/or linear combinations of these functions.
 5. The method as claimedin claim 1, wherein said substep of taking into account at least spatialcharacteristics of said reproduction unit is carried out at least withthe help of parameters representative, for each element, of the threecoordinates of its position with respect to the center placed in thelistening zone, and/or of its spatio-temporal response.
 6. The method asclaimed in claim 5, wherein said substep of taking into account at leastspatial characteristics of said reproduction unit is carried outmoreover with the help: of parameters describing, in the form ofweighting coefficients, a spatial window which specifies thedistribution in space of reconstruction constraints for the acousticfield; and of a parameter describing an order of operation limiting thenumber of coefficients to be taken into account during said step ofdetermining reconstruction filters.
 7. The method as claimed in claim 5,wherein said substep of taking into account characteristics of saidreproduction unit is carried out moreover with the help: of parametersconstituting a list of spatio-temporal functions whose reconstruction isimposed; and of a parameter describing an order of operation limitingthe number of coefficients to be taken into account during said step ofdetermining reconstruction filters.
 8. The method as claimed in one ofclaims 5, wherein said step of taking into account at least spatialcharacteristics of said reproduction unit is carried out moreover atleast with the help of one of the parameters chosen from the groupconsisting: of parameters representative of at least one of the threecoordinates of the position of each or some of the elements, withrespect to the center placed in the listening zone; of parametersrepresentative of the spatio-temporal responses of each or some of theelements; of a parameter describing an order of operation limiting thenumber of coefficients to be taken into account during said step ofdetermining reconstruction filters; of parameters constituting a list ofspatio-temporal functions whose reconstruction is imposed; of parametersrepresentative of the templates of said reproduction elements; of aparameter representative of the desired local capacity of adaptation tothe spatial irregularity of the configuration of said reproduction unit;of a parameter defining the radiation model for said reproductionelements; of parameters representative of the frequency response of saidreproduction elements; of a parameter representative of a spatialwindow; of parameters representative of a spatial window in the form ofweighting coefficients; and of a parameter representative of the radiusof a spatial window when the latter is a ball.
 9. The method as claimedin claim 5, wherein it comprises a calibration step making it possibleto deliver all or part of the parameters used in said step ofdetermining reconstruction filters.
 10. The method as claimed in claim9, wherein said calibration step comprises, for at least one of thereproduction elements: a substep of acquiring signals representative ofthe radiation of said at least one element in the listening region (4);and a substep of determining spatial and/or acoustic parameters of saidat least one element.
 11. The method as claimed in claim 10, whereinsaid calibration step comprises: a substep of emitting a specific signalto said at least one element of said reproduction unit, said acquisitionsubstep corresponding to the acquisition of the sound wave emitted inresponse by said at least one element; and a substep of transformingsaid signals acquired into a finite number of coefficientsrepresentative of the sound wave emitted, so as to allow the carryingout of said substep of determining spatial and/or acoustic parameters.12. The method as claimed in claim 10, wherein said acquisition substepcorresponds to a substep of receiving a number of coefficientsrepresentative of the acoustic field generated by said at least oneelement in the form of a linear combination of spatio-temporalfunctions, which coefficients are used directly during said substep ofdetermining spatial and/or acoustic parameters of said at least oneelement.
 13. The method as claimed in claim 9, wherein said calibrationsubstep furthermore comprises a substep of determining the position inat least one of the three dimensions in space of said at least oneelement of said reproduction unit.
 14. The method as claimed in claim 9,wherein said calibration step furthermore comprises a substep ofdetermining the spatio-temporal response of said at least one element ofsaid reproduction unit.
 15. The method as claimed in claim 9, whereinsaid calibration step furthermore comprises a substep of determining thefrequency response of said at least one element of said reproductionunit.
 16. The method as claimed in claim 1, wherein it comprises a stepof simulating all or part of the parameters necessary for carrying outsaid step of determining reconstruction filters.
 17. The method asclaimed in claim 16, wherein said simulation step comprises: a substepof determining missing parameters from among the parameters used duringsaid step of determining reconstruction filters; a plurality ofcalculation substeps making it possible to determine the value or valuesof the missing parameter or parameters as defined previously as afunction of the parameters received, of the frequency, and ofpredetermined default parameters.
 18. The method as claimed in claim 17,wherein said simulation step comprises a substep of determining a listof elements of the reproduction unit that are active as a function ofthe frequency, and in that said calculation substeps are carried outjust for the elements of said list.
 19. The method as claimed in claim17, wherein said simulation step comprises a substep of calculating aparameter representative of the order of operation limiting the numberof coefficients to be taken into account during said step of determiningreconstruction filters with the help of at least the position in spaceof all or part of the elements of the reproduction unit.
 20. The methodas claimed in claim 17, wherein said simulation step comprises a step ofdetermining parameters representative of a spatial window in the form ofweighting coefficients with the help of a parameter representative ofthe spatial window in the spherical reference frame and/or of aparameter representative of the radius of said spatial window when thelatter is a ball.
 21. The method as claimed in claim 17, wherein saidsimulation step comprises a substep of determining a list ofspatio-temporal functions whose reconstruction is imposed with the helpof the position of all or part of the elements of the reproduction unit.22. The method as claimed in claim 1, wherein it comprises a step ofinput making it possible to determine all or part of the parameters usedduring said step of determining reconstruction filters.
 23. The methodas claimed in claim 1, wherein said step of determining reconstructionfilters comprises: a plurality of calculation substeps carried out for afinite number of frequencies of operation and making it possible todeliver a matrix for weighting the acoustic field, a matrixrepresentative of the radiation of the reproduction unit, and a matrixrepresentative of the spatio-temporal functions whose reconstruction isimposed; and a substep of calculating a decoding matrix, carried out fora finite number of operating frequencies, with the help of the matrixfor weighting the acoustic field, of the matrix representative of theradiation of the reproduction unit, of the matrix representative of thespatio-temporal functions whose reconstruction is imposed, and of aparameter representative of the desired local capacity of adaptation tothe spatial irregularity of the reproduction unit, representative of thereconstruction filters.
 24. The method as claimed in claim 23, whereinsaid calculation substep making it possible to deliver a matrixrepresentative of the radiation of the reproduction unit is carried outwith the help of parameters representative for each element: of thethree coordinates of its position with respect to the center placed inthe listening zone; and/or of its spatio-temporal response.
 25. Themethod as claimed in claim 24, wherein said calculation substep makingit possible to deliver a matrix representative of the radiation of thereproduction unit is carried out moreover with the help of parametersrepresentative for each element of its frequency response.
 26. Acomputer program comprising program code instructions for the executionof the steps of the method as claimed in claim 1, when said program isexecuted on a computer.
 27. A removable medium of the type comprising atleast one processor and a nonvolatile memory element, wherein saidmemory comprises a program comprising instructions for the execution ofthe steps of the method as claimed in claim 1, when said processorexecutes said program.
 28. A device for controlling a reproduction unitfor restoring an acoustic field, comprising a plurality of reproductionelements, wherein it comprises at least: means of determiningreconstruction filters representative of said reproduction unit, adaptedso as to make it possible to take into account at least spatialcharacteristics of said reproduction unit; and means for determining atleast one control signal (sc₁ to sc_(N)) for said elements of saidreproduction unit, said at least one signal being obtained byapplication of said reconstruction filters to a finite number ofcoefficients representative of the distribution in time and in the threedimensions in space of said acoustic field to be reproduced.
 29. Thedevice as claimed in claim 28, wherein it is associated with means forshaping an input signal comprising temporal and spatial information fora sound environment to be reproduced, which means are adapted fordecomposing said information over a basis of spatio-temporal functionsso as to deliver a signal comprising said finite number of coefficientsrepresentative of the distribution in time and in the three dimensionsin space of said acoustic field to be reproduced, corresponding to saidsound environment, in the form of a linear combination of saidspatio-temporal functions.
 30. The device as claimed in claim 29,wherein said spatio-temporal functions are so-called Fourier-Besselfunctions and/or linear combinations of these functions.
 31. The deviceas claimed in claim 28, wherein said means for determiningreconstruction filters receive as input at least one of the parametersfrom the following parameters: parameters representative of at least oneof the three coordinates of the position of each or some of theelements, with respect to the center placed in the listening zone;parameters representative of the spatio-temporal responses of each ofsome of the elements; a parameter describing an order of operationlimiting the number of coefficients to be taken into account in themeans of determining reconstruction filters; parameters representativeof the templates of said reproduction elements; a parameterrepresentative of the desired local capacity of adaptation to thespatial irregularity of the configuration of said reproduction unit; aparameter defining the radiation model for said reproduction elements;parameters representative of the frequency response of said reproductionelements; a parameter representative of a spatial window; parametersrepresentative of a spatial window in the form of weightingcoefficients; a parameter representative of the radius of a spatialwindow when the latter is a ball; and parameters constituting a list ofspatio-temporal functions whose reconstruction is imposed.
 32. Thedevice as claimed in claim 28, wherein each of said parameters receivedby said means of determining reconstruction filters is conveyed by oneof the signals from the group of the following signals: a definitionsignal comprising information representative of the spatialcharacteristics of the reproduction unit; a supplementary signalcomprising information representative of the acoustic characteristicsassociated with the elements of the reproduction unit; and anoptimization signal comprising information relating to an optimizationstrategy, so as to deliver, with the aid of the parameters contained inthese signals, a signal representative of said reconstruction filtersrepresentative of said reproduction unit.
 33. The device as claimed inclaim 32, wherein it is associated with means for determining all orpart of the parameters received by said means for determiningreconstruction filters, said means comprising at least one of thefollowing elements: simulation means; calibration means; parametersinput means.
 34. The device as claimed in claim 28, characterized inthat said means for determining reconstruction filters are adapted fordetermining a set of filters representative of the position in space ofthe elements of the reproduction unit.
 35. The device as claimed inclaim 28, wherein said means of determining reconstruction filters areadapted for determining a set of filters representative of the roomeffect induced by the listening zone.